Virgin Trains Ticketing is not run by a train company, but can be slightly buggy now and then, but comes with a rewards scheme that you can use to buy train tickets or other stuff with (Virgin Red Points)
I can also second the forum's site, though it charges a share of savings if it identifies split ticket savings and you use them, the level of attention to detail in its design is second to none. Download the Trainsplit app (it's powered by trainsplit) if you want a mobile app experience.
But as
@Sonic1234 has said, if you truly value privacy, buy from the TVM or ticket office, paying cash if you
really want privacy.